Information on Result #1301764

Linear OA(5116, 78171, F5, 19) (dual of [78171, 78055, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(5115, 78169, F5, 19) (dual of [78169, 78054, 20]-code), using
    • construction X applied to Ce(18) ⊂ Ce(12) [i] based on
      1. linear OA(5106, 78125, F5, 19) (dual of [78125, 78019, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(571, 78125, F5, 13) (dual of [78125, 78054, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
  2. linear OA(5115, 78170, F5, 18) (dual of [78170, 78055, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 5115 > Vbs−1(k−1) = 7 324985 381039 151986 424044 094291 832093 164735 069191 012855 217999 523671 794980 965157 [i]
  3. linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(5116, 78171, F5, 2, 19) (dual of [(78171, 2), 156226, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5116, 78171, F5, 3, 19) (dual of [(78171, 3), 234397, 20]-NRT-code) [i]
3Digital (97, 116, 78171)-net over F5 [i]